The centre of gravity of a uniform solid right circular cone of height h lies on its axis at a distance of
- A.h divided by 2 from the base
- B.h divided by 3 from the base
- C.h divided by 4 from the base
- D.3h divided by 4 from the base
Correct answer
Explanation
The correct answer is C, h divided by 4 from the base. A solid cone has more material near its wide base than near its apex, so its centre of gravity lies on the axis of symmetry well below the middle, at one quarter of the height measured from the base, which is three quarters of the height measured down from the apex. Option A is wrong because half the height is the centre of gravity of a uniform cylinder, where the cross section does not change along the axis. Option B is wrong on two counts: one third of the height from the base is the centroid of a triangular lamina, and it is also the centre of gravity of a hollow cone, that is of a conical shell, which is a favourite distractor here. Option D is wrong because it measures the same point from the wrong end; h divided by 4 is from the base and 3h divided by 4 from the apex.
Read the full article: Centre of Gravity, Torque and Equilibrium: Exam Notes
Practice Questions
View allWhat is the SI unit of torque?
- A.Newton
- B.Newton metre
- C.Newton per metre
- D.Joule per second
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Torque is the product of a force and the perpendicular distance of its line of action from the axis of rotation, so its unit is the unit of force multiplied by the unit of length, the newton metre, and its dimensional formula is M L squared T to the power…
Read the full explanation →Three forces acting on a rigid body are represented in magnitude, direction and line of action by the three sides of a triangle taken in order. The forces are equivalent to a couple whose moment is equal to
- A.Thrice the area of the triangle
- B.Twice the area of the triangle
- C.The area of the triangle
- D.Half the area of the triangle
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When three forces are represented by the sides of a triangle taken in order, their vector sum is zero, because the three sides close the triangle, so the body cannot be pushed away; but the lines of action are different, so the system reduces to a couple.
Read the full explanation →The centre of gravity of a uniform circular ring lies
- A.On the ring itself, at any point
- B.At the centre of the ring, outside its material
- C.At one third of the radius from the centre
- D.Nowhere, because a ring has no centre of gravity
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The centre of gravity is a geometrical point through which the resultant weight of a body acts, and by symmetry that point for a uniform ring is its geometrical centre, which lies in the empty space inside the ring.
Read the full explanation →The torque produced by a force about an axis is maximum when the angle between the force and the arm is
- A.0 degree
- B.45 degrees
- C.90 degrees
- D.180 degrees
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The magnitude of torque is r into F into the sine of the angle between the arm and the force, and the sine of an angle is largest, equal to one, at 90 degrees, so the whole of the force is then used in turning the body.
Read the full explanation →A long spanner loosens a tight nut more easily than a short one because it
- A.Reduces the force needed by increasing the moment arm
- B.Reduces the friction at the nut
- C.Increases the mass acting on the nut
- D.Changes the direction of the weight of the nut
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Torque is the product of the force and the perpendicular distance of its line of action from the axis, so the same turning effect can be produced by a smaller force if that distance is made larger; a long handle therefore does the same work with less effort.
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